The domain of definition of the function f(x) | vedclass

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Question

(D) Given the equation $2^x + 2^y = 2$. Rearranging for $2^y$,we get $2^y = 2 - 2^x$. Taking the logarithm base $2$ on both sides,$y = \log_2(2 - 2^x)

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$-\infty < x < 1$

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(D) Given the equation $2^x + 2^y = 2$. Rearranging for $2^y$,we get $2^y = 2 - 2^x$. Taking the logarithm base $2$ on both sides,$y = \log_2(2 - 2^x)$. For the function to be defined,the argument of the logarithm must be strictly positive: $2 - 2^x > 0$. This implies $2^x Since $2 = 2^1$,we have $2^x Since the base $2 > 1$,the inequality holds for $x Thus,the domain is $(-\infty, 1)$,which is written as $-\infty < x < 1$.

The domain of definition of the function $f(x)$ given by the equation $2^x + 2^y = 2$ is

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